Tina, however frequently cooks in her kitchen; Carlos never eats.

Question

How would you correctly punctuate this? Why is there a comma after Tina? 

Answer 1

The comma after Tina is to separate the word "however" from the rest of the clause which is interrupts. For the same reason, there should also be a comma after the word "however". the semicolon (;) after kitchen is correct, since it separates two independent clauses, which could be sentences that make sense on their own.